In geometrically similar models, kinematic similarity is assured when 

 there is dynamic similarity. 



Two systems are dynamically similar if there is similarity of masses 

 and forces (i.e., if there is kinematic similarity, if the ratios of the 

 masses of the varioiis homologous particles or objects that are involved 

 in the motion occurrences are equal, and if the ratios of the homologous 

 forces that affect the motion occurrence of the homologous objects are 

 equal). Thus, 



Mm = M,M^ (2-3) 



and 



Fm = FrFp • (2-4) 



In the types of fluid mechanics problems involved in coastal and estuarine 

 engineering projects, the forces on system elements consist of the kinetic 

 reaction due to the inertia of an element's mass (Fi) , gravity (Fg) , 

 viscous shear (F^) ,, surface tension (Fst), elastic compression (Fe) , 

 and the pressure force resulting from or connected with the motion (Fpr) . 

 It follows from Newton's second law of motion that the vector sum of the 

 active forces on an element is equal to the element's mass reaction to 

 those forces, 



Fi = Fg + F^ + F^^ + F^ + Fp^ . (2-5) 



For overall similarity, the ratio of the inertia forces, model to proto- 

 type, must equal the ratio of the vector sum of the active forces. 



(F07 " (Fg * F. * F3, . F, + F^,)_^ • 



Also, dynamic similitude is not obtained unless 



(l!L (SL ^ (Mb (^ (^p4 



(2-6) 



(2-7) 



All but one of these ratios may be regarded as independent quantities, 

 with that one ratio being determined after the others are established. 

 The pressure ratio is usually regarded as the dependent variable; thus, 

 it is not used in the process of determining the scale relationship for 

 the type of studies under consideration (Warnock, 1950). However, there 

 are other types of hydraulic flow problems in which the pressure force 

 is a primary variable and is used in determining the scale relationships, 

 model to prototype. 



No model fluid is known that has viscosity, surface tension, and 

 elastic modulus characteristics such as to satisfy equation 2-7. How- 

 ever, since one or more of the forces may not contribute to the flow 

 phenomenon under consideration, and others may have only a slight effect 



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